I go at it from a cleanliness point. Rubber mats are easier to clean, get everything up off the floor, summer and winter. Keeps the protective layer of mat from letting floor get holes or uneven. This means horse is standing and laying on a dry layer, if using a good amount of bedding. Floor is level to let him stand evenly, not up and down hill in holes. I can clean the mat, sweep up everything, no urine wetness left like with dirt floors. No frozen spots that are uncleanable for him to lay on come winter. Mat insulates him from floor cold sucking body heat, along with bedding layer padding, should horse want to lay down in the cold times.
I have only had one barn I rented with a dirt floor and I hated it. Could NOT keep the floor leveled or clean, with everything freezing to the dirt.
I would rather clean cement and double the bedding bill, than fight cleaning dirt floors, especially in winter. Even wood plank floors are better than dirt, though they do need replacing if horses are shod and wear down the wood. Finally getting our own barn, we got rubber mats and enjoy the benefits they give our stalled horses and ESPECIALLY the easy stall cleaning.
I know of no actual study of floor mat advantages, but there must be something out there. People LOVE doing studies.
Almost no one keeps horses on dirt floors anymore after they have used stall mats!
Congrats on your newly matted stalls.